A123086 - OEIS

%I #16 Feb 25 2013 00:18:35

%S 11860710,19524458,30466003,57980974,63924288,90876871,98124660,

%T 100711080,107813124,130902871,130920140,133345096,137765645,

%U 149928192,187600902,214934436,223349020,235566127,238768532,239934902,264189816,270196572,278851320,285021997

%N Numbers which are the arithmetic mean of 1000000 consecutive primes.

%C Corresponding indices of the first primes are: 275775, 740092, 1383476, 2948575, 3280201, 4764532, 5159226, 5299723, 5684491, 6926061, 6926985, 7056669, 7292768, 7940227, 9929283, 11358606, 11796712, 12431386, 12597486, 12657959, 13911879, 14221421, 14666768, 14983910, 15100050.

%H Zak Seidov, <a href="/A123086/b123086.txt">Table of n, a(n) for n = 1..467</a>

%e 11860710 is in the sequence since (p(275775) + p(275776) + ... + p(275775+999998) + p(275775+999999)) / 1000000 = 11860710 where p(n) is the n-th prime.

%t Timing[s = 7472966967499 ; a = 2; b = 15485863; Do[s = s - a + (b = NextPrime[b]); a = NextPrime[a]; If[Mod[s, 10^6] < 1, Print[s/10^6]], {10^8}]]

%o (PARI){s = 7472966967499 ; a = 2; b = 15485863; for (k = 1, 10^9,

%o if(s%10^6 < 1, print( s/10^6)); b = nextprime (b + 2);

%o s = s - a + b; a = nextprime (a + 1))}

%Y Cf. A102655 (arithmetic mean of four successive primes).

%Y Cf. A122040 (arithmetic mean of six successive primes).

%Y Cf. A122480 (arithmetic mean of k consecutive primes).

%Y Cf. A122808 (arithmetic mean of n, but no fewer, consecutive primes).

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 27 2006